Microscopic-macroscopic Entanglement Transfer In Non-Markovian Environment

Quantum entanglement is a very wonderful phenomenon in quantum mechanics.People have never stopped arguing about it since the concept was put forward.Quantum entanglement is ubiquitous in microscopic particles,but it is hard to be oberserved in the macroscopic world.This is because decoherence inevitably occurs when the system interacts with the environment.We can realize microscopic-macroscopic entanglement transfer by means of optomechanical system.One may be able to solve the essential problems of quantum mechanics by observing the macroscopic entanglement.Optomechanical system is a rising discipline in recent decades.It can be used for weak force measurement and single atom manipulation because of its high quality factor and super high sensitivity.Besides,optomechanical system is also used in gravitational wave detection device.The Non-Markovian process has an extremely wide range of applications in mathematics and physics.Non-Markovian environment refers to the information flowing from the system to the environment can be partially returned to the system when the system and the environment interact with each other.Namely,the environment has a feedback to the system.Because of such a feedback that the information dissipated into the environment can be partially refluxed,the decoherence process can be delayed.The theoretical model we consider in this paper is two coupled cavities simulated by a superconducting circuit(LC circuit)with two vibrating capacitors connected to each cavity,which can be regarded as a macroscopic oscillator.The system is considered in a non-Markov environment,while the strength of non-Markovian environment can be measured by memory time.The greater the memory time,the more obvious the non-Markovian effect is.When memory time tends to zero,the environment degenerates from non-Markovian to Markovian.It is found that the longer the memory time is,the more information is fed back from the environment to the system,and thus the entanglement transfer from cavities to oscillators can be enhanced.We also found that when the memory time is longer,the entanglement experiences a recovery process after sudden death.It is precisely because of the repeating emergence of entanglement resuscitation that entanglement remains for a long time and the decoherence problem is effectively delayed.On the contrary,there is no entanglement resuscitation when memory time is less.In addition,we also study the relationship between memory time and entanglement transfer speed.It is found that the longer memory time is,the slower the entanglement transfer is,but the ratio of the maximum entanglement transfer could be larger.Finally,we investigate the effect of other parameters on entanglement in the model.The entanglement transfer varies with the coupling strength of the cavities.This requires us to select appropriate parameters in the process of entanglement transfer and we can achieve the maximum entanglement transfer.